Tough- plastic deformation
Strong- ability to resist bending
Soft steels can be very tough but not strong. Hard steels can be strong and resist bending (like for prying) but won't deform, instead they break.
Like mentioned above, a nice balance is ideal. Though with modern cpm steels I think strength is over shadowing toughness.
Look at Nathan's d3v. It won't bend and take a set, but you'll have a hell of a time breaking it.
Edge retention goes up with hardness. Obviously many other factors play into edge retention like geometry, toughness and strength.
All of this is in general and in layman's terms.